Manifolds and Mechanics

Fülszöveg

This book provides an easy introduction to the theory of differentiable manifolds. The authors then show how the theory can be used to develop, simply but rigorously, the theory of Lagrangian mechanics directly from Newton's laws. Unnecessary abstraction has been avoided to produce an account suitable for students in mathematics or physics who have taken courses in advanced calculus. Clearly but intuitively defined geometric notions have replaced those concepts of Lagrangian mechanics that are usually vaguely defined. Consequently, the book is also a thorough but basic account of modern mechanics; at the same time applications of the theory to some classical problems are also given.
AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES
Editor-in-Chief: Dr. S.A. Morris, Department of Mathematics, LaTrobe University, Bundoora, Victoria3083, Australia
Editors:
Professor C.J.Thompson, Department of Mathematics, University of Melbourne, Parkville, Victoria3052, Australia
ProfessorC.C.... Tovább

Fülszöveg

This book provides an easy introduction to the theory of differentiable manifolds. The authors then show how the theory can be used to develop, simply but rigorously, the theory of Lagrangian mechanics directly from Newton's laws. Unnecessary abstraction has been avoided to produce an account suitable for students in mathematics or physics who have taken courses in advanced calculus. Clearly but intuitively defined geometric notions have replaced those concepts of Lagrangian mechanics that are usually vaguely defined. Consequently, the book is also a thorough but basic account of modern mechanics; at the same time applications of the theory to some classical problems are also given.
AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES
Editor-in-Chief: Dr. S.A. Morris, Department of Mathematics, LaTrobe University, Bundoora, Victoria3083, Australia
Editors:
Professor C.J.Thompson, Department of Mathematics, University of Melbourne, Parkville, Victoria3052, Australia
ProfessorC.C. Heyde, Department of Statistics, University of Melbourne, Parkville, Victoria 3052, Australia
Professor J.H. Loxton, Department of Pure Mathematics, University of New South Wales, Kensington, New South Wales 2033, Australia
The Australian Mathematical Society Lecture Series is intended to operate at the frontiers of mathematics itself and of its teaching, and therefore will contain both research monographs and textbooks suitable for graduate or undergraduate students.
Cover design: Ken Vail
Cambridge University Press Vissza